Simple Analytics of the Government Expenditure Multiplier

This paper explains the key factors that determine the effectiveness of government purchases as a means of increasing output and employment in New Keynesian models, through a series of simple examples that can be solved analytically. Delays in the adjustment of prices or wages can allow for larger multipliers than exist in the case of fully flexible prices and wages; in a fairly broad class of simple models, the multiplier is 1 in the case that the monetary authority maintains a constant path for real interest rates. The multiplier can be considerably smaller, however, if the monetary authority raises real interest rates in response to increases in inflation or real activity resulting from the fiscal stimulus. A large multiplier is especially plausible when monetary policy is constrained by the zero lower bound on nominal interest rates; in such a case, expected utility is maximized by expanding government purchases to at least partially fill the output gap that would otherwise exist owing to the central bank's inability to cut interest rates. However, it is important in such a case that neither the increased government purchases nor the increased taxes required to finance them be expected to persist beyond the period over which monetary policy is constrained by the zero lower bound. Michael Woodford Department of Economics Columbia University 420 W. 118th Street New York, NY 10027 and NBER [email protected] The recent worldwide economic crisis has brought renewed attention to the question of the usefulness of government spending as a way of stimulating aggregate economic activity and employment during a slump. Interest in fiscal stimulus as an option has been greatly increased by the fact that in many countries by the end of 2008, the short-term nominal interest rate used as the main operating target for monetary policy had reached zero — or at any rate, some very low value regarded as an effective lower bound by the central bank in question — so that further interest rate cuts were no longer available to stave off spiraling unemployment and fears of economic collapse. Increases in government spending were at least a dimension on which it was possible for governments to do more — but how effective should this be expected to be as a remedy? Much public discussion of this issue has been based on old-fashioned models (both Keynesian and anti-Keynesian) that take little account of the role of intertemporal optimization and expectations in the determination of aggregate economic activity. Yet discussions of monetary stabilization policy over the past several decades have been transformed by the development of a new generation of macroeconomic models that simultaneously consider the dynamic implications of intertemporal optimization on the one hand, and delays in the adjustment of wages and prices on the other. The implications of these models for fiscal stabilization policy have been much less fully developed than their implications for monetary policy. But this is not because the models do not have implications for fiscal policy. The present paper reviews some of these implications for one specific question of current interest: the determinants of the size of the effect on aggregate output of an increase in government purchases, or what has been known since Keynes (1936) as the government expenditure “multiplier.” I discuss this issue in the context of a series of models that are each simple enough for the effects to be computed analytically, so that the consequences of parameter variation for the quantitative results will be completely clear. It is hoped that the economic mechanisms behind the various results will be fairly transparent as well. I also restrict my attention to policy experiments that are defined in such a way that the time path of the increase in output has the same shape as the time path of the increase in government purchases, so that there is a clear meaning to the calculation of a “multiplier” (though more generally this need not be the case). These models are too simple to be taken seriously as the basis for quantitative estimates of the effects of some actually contemplated policy change; nonetheless, I believe that the mechanisms displayed in these simple examples explain many of the numerical results